Under what circumstances does trade yield Pareto-inferior results?

Question

The usual assumption is that free trade always increases aggregate gains. This has in fact been proven for various models of trade between countries, though there are counterexamples if one makes different assumptions.

I believe the following is a rather simple counterexample that relies on even fewer assumptions, and in particular uses Braess's paradox rather than dynamic expectations:

Suppose we have two countries, hypothetically named US and China (any resemblance to actual countries is purely coincidental). Each independently produces a single type of good called "phones". Production of phones is a two-step process: first, the phone is designed by engineers, then it is built by factory workers.

In the initial scenario, there is no trade: each country produces 1400 phones on its own.

In the US, engineers are efficient and factory workers are scarce; to produce one phone costs \$100 of engineering time for the design and $200 to be built by factory workers.

In China, engineers are less efficient and factory workers are available in abundance; to produce one phone costs \$200 of engineering time for the design and $100 to be built by factory workers.

Now, suppose trade opens up between the US and China. So now, 2800 phones are designed in the US and built in China.

However, let's assume the supply curves for each type of labor slope upward (as is usually the case). In particular, in order to attract enough US engineers to design 2800 phones, US engineering wages go up to \$175/phone. Likewise, in order to attract enough Chinese factory workers to build 2800 phones, factory wages in China rise to $175/phone. At the same time, US factory wages fall to \$185/phone, and China engineering wages fall to \$185/phone.

So far, we are still Pareto-efficient, since the increased wages allow US Engineers and Chinese factory workers to buy the same 2800 phones that were bought before; equivalently, a government with full knowledge of preferences could redistribute money (or phones) to make everyone as well off as they were before trade.

But now, assume that cross-Pacific collaboration incurs an additional \$5/phone cost, eg for undersea cables. Phones now cost \$355, but aggregate income is only \$350*2800=\$980,000, ie not enough for 2800 phones. I believe that only distortionary taxation/subsidies can bring everyone back to their previous welfare, eg taxing US Engineers enough to make trade unprofitable.

Is my analysis correct, ie is this a genuine theoretical counter-example? Is there a particular reason to expect this type of situation would be rare? Consider that Braess's paradox has been found to occur in 50% of networks, under certain simple assumptions.

Assuming my analysis is correct, is this phenomenon well-known? Can you point me to relevant literature on similar ideas?

Before trade:

With trade:

(apologies for my limited diagramming skills)

EDIT: here's what happens in terms of actual resources:

In the US, assume you have 100 "engineer" workers who are each able to use US technology to design 14 phones; and you have 200 "factory" workers who are each able to build 7 phones. In China, you have 200 engineers who can each design 7 phones, and 100 factory workers who can each build 14 phones.

US Engineers cannot build, and Chinese factory workers cannot design.

175 of the US factory workers can also design, though only 8 phones each

175 of the Chinese engineers can also build, but only 8 phones each

So, under autarky we produce 2800 phones (1400 in each country).

Under free trade we still produce 2800 phones (designed in the US and built in China), though we leave 25 US factory workers and 25 Chinese engineers unemployed.

But now, assume that transmitting designs for up to 560 phones from the US to China (and training overseas workers) requires one US engineer and one Chinese factory worker. Furthermore, assume that there is a minimum wage in both countries, so the unemployed workers cannot be profitably employed, nor benefit from their unemployment.

We can now only produce 2730 phones, and no lump-sum redistribution can recover previous welfare levels.

Answer 1

After more thought and research, I am fairly confident in saying the basic analysis holds, ie this is a "counter-example" in the sense that trade yields Pareto-inferior results. The result relies on the existence of some market distortion; trade can reduce aggregate welfare when it makes the distortion worse. The distortion can take various forms:

• If there is a minimum wage, trade can force more people to be unemployed who would prefer to work for sub-minimum wage.
• If there is any kind of externality or "congestion effect", trade can exacerbate this; for example, it's easy to convert the scenario to one where the materials cost of housing for engineers or factory workers rises with density, and again trade lowers aggregate welfare
• In the presence of finite credit markets, free trade could redirect investment in a way that reduces aggregate welfare (this could be observed as an "infant industry" effect).
• In the dynamic counterexample of Willmann (2003), the distortion is underinvestment aimed at affecting redistribution
• In Markusen (1980) (PDF), in the presence of increasing returns to scale, monopoly can be exacerbated by trade, though not in a stable equilibrium
• In Helpman and Krugman (1985), as cited by Feenstra (2004), we have a fairly general set of conditions for trade to increase aggregate welfare in the presence of some distortions, including the provision that "world output of each differentiated goods industry does not contract." To me this condition appears to somewhat beg the question, and I see no inherent reason to assume it would be fulfilled more than about half the time in the presence of arbitrary distortions.
• Partial trade reform, including regional trade agreements, can be more complicated (see ch 9 of Feenstra (2004), though I haven't studied it all yet)

Furthermore, even when trade does result in Pareto-superior results / gains in aggregate welfare, the redistribution that would be required to actually make everyone better off is not only potentially difficult politically, but often actually impossible to implement, eg requiring perfect knowledge of unrevealed preferences (Facchini & Willman (2001)).

Personally, this seems to tell a very different story than the popular conception of the economics profession's view on trade, and the narrative I got from my undergraduate International Trade course (at a prestigious US research university), which focused on distortion-free static models like the basic Heckscher-Ohlin and suggested that while there were losers from trade, by and large it was expected to yield aggregate gains. It seems to me that in practice, distortions like the above are rather the norm, and so reflexive advocacy of trade liberalization should perhaps consider the potential for exacerbating distortions in any particular case.